Hello.
This formula is equivalent to the one proposed in the original article. Here’s why:
In the above, PA is the PVI.
PA = P’B
P’B = NB - NP’ => PA = NB - NP’
But:
NB = ON * sin(α) = NIR_value * sin(α)
NP’ = NP * cos(α) = OR * cos(α) = RED_value * cos(α)
Hence:
PA = NIR_value * sin(α) - RED_value * cos(α)
In the original article, PVI = sqrt((Rgg5 - Rp5)^2 + (Rgg7 - Rp7)^2)
Rgg5 and Rgg7 are the coordinates of the A point in the figure above.
Rp5 and Rp7 are the coordinates of the P point in the figure above.
Then, the sqrt formula is, in fact, the distance between the points P and A, which is, in our case, the PA segment.
What has been introduced in SNAP are the weights of the two values (NIR, RED). Using the default value of 1.0 leads to the original formula.
Hope this clears things for you.
Cheers.